On the generalized Nielsen realization problem

Details On the generalized Nielsen realization problem On the generalized Nielsen realization problem

2005-08-08

arxiv.org/abs/math/0508135v1

Mathematics

Geometric Topology

Scientific paper

The main goal of this paper is to give the first examples of equivariant aspherical Poincare complexes, that are not realized by group actions on closed aspherical manifolds $M$. These will also provide new counterexamples to the Nielsen realization problem about lifting homotopy actions of finite groups to honest group actions. Our examples show that one cannot guarantee that a given action of a finitely generated group $\pi$ on Euclidean space extends to an action of $\Pi$, a group containing $\pi$ as a subgroup of finite index, even when all the torsion of $\Pi$ lives in $\pi$.

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